1. Field of the Invention
The present invention relates to the domain of image processing methods. It concerns a method for approximating a circular spread function in a computationally efficient way. It can be used in image processing for printing three-dimensional objects by means of for example inkjet printing. The method is particularly suited for the case where the three-dimensional object is a three-dimensional relief print master. Such a print master is created by calculating a plurality of intermediate image layers using the invented method and printing these layers on top of each other.
The present invention also relates to a corresponding apparatus. Such an apparatus may be used for a wide array of applications, for example for the manufacture of stamps, flexographic, letterpress or gravure print masters.
2. Description of the Related Art
Three-dimensional printing is a method for creating three-dimensional objects by depositing or forming thin layers of material in succession on top of each other so as to build up the desired three-dimensional structure. It is sometimes called “Rapid Prototyping and Manufacturing” (RP&M).
Various methods have been devised to create the thin layers.
One technique makes use of a bath of polymerisable liquid material. A thin upper layer of the liquid is cross-linked or hardened in some way, e.g. via laser light in a pattern which is the same as a cross-section through the object to be formed. The laser spot is moved across the surface in accordance with a digital representation of the relevant cross section. After one layer is completed, the liquid level is raised over a small distance and the process is repeated. Each polymerised layer should be sufficiently form-stable to support the next layer.
In another technique powder is dusted onto a substrate and the powder is coalesced by some means, e.g. by heating or by the use of a liquid hardener, in accordance with the shape of the cross-section of the object to be formed.
In yet another method, cross linkable or hardenable material is deposited in the form of drops which are deposited in a pattern according to the relevant cross-section of the object to be formed.
Still another method involves dispensing drops of molten material at an elevated temperature which then solidify on contact with the cooler work piece.
There are many items which can be reproduced by three-dimensional printing. Due to the fact that the materials used to form the object are subject to many limitations and are generally polymeric in nature, the final product is not very strong. Therefore three-dimensional printing is usually reserved for prototyping, for example to create a product design which can be handled or even tested for certain properties.
More information on rapid prototyping, three-dimensional printing, additive fabrication, tooling, and rapid manufacturing is also found in the Wohlers Report 2008, edited and published by Wohlers Associates, Inc., OakRidge Business Park 1511 River Oak Drive in Fort Collins, Colo. 80525 USA.
Printing plates (also referred to as print masters or print forms) are traditionally manufactured using a combination of image wise exposure by a laser or light source followed by a chemical or physical developing step. Such plates are used in a variety of printing methods, such as flexographic printing, letterpress, offset or gravure printing.
Flexographic printing or flexography is a printing process where a flexible print master transfers a fast drying fluid to the printable substrate. The print master can be a flexible plate mounted on a cylinder or a cylindrical sleeve. Flexographic printing plates have the features that define the image that is to be printed in relief, which means that the ink printing area is raised relative to the non ink printing area. The result is a relief plate that is capable of transferring ink from an anilox roll to a substrate. An advantage of flexographic printing is that almost any material that can run through a web press can be printed on in this way, including hard surfaced material such as acetate and other plastic films. Flexography has also been known as “aniline” printing because of the aniline dye inks that were originally used in the process.
Letterpress is a printing process where the image is raised as well and inked to produce an impression.
Offset printing is a method of printing in which the image is not printed directly from a plate, but is offset onto a cylinder which performs the actual printing operation. The printing plate generally has image-selective hydrophobic regions on a hydrophilic background.
Gravure printing is a printing process where the image is etched into a plate or cylinder in the form of recesses or wells. These recesses or wells are filled with ink and the remaining surface is wiped off, thus leaving the ink only in the recesses or wells. The image can then be printed off e.g. onto an absorbent material such as paper.
There are several additional methods of transferring an image from a printing plate onto the printing medium. For instance in tampon printing, a plate comprising an image in relief (or a negative image as in gravure printing) is inked. Afterwards, ink is transferred to a soft tampon printing head by contacting the tampon surface with the inked image. The tampon is then used to print another object, e.g. an object with an irregular surface.
Except in offset printing, relief print masters are used which comprise a substrate with raised parts and recesses. In some of the printing methods such as in flexography and letterpress, the raised parts are used for forming the image, while in gravure printing the recesses form the image. In tampon printing either can be used.
The smallest individual raised portions on a flexographic printing plate are particularly vulnerable to damage. One form of damage is Euler buckling. Euler buckling is the buckling of a thin column into a bow-like or wave-like shape. Assuming a raised portion of a flexographic printing plate has a cylindrical shape having a height H and a diameter d, the critical load which can be applied before buckling is initiated varies approximately as:
                              P          CR                =                                            π              2                        *            E            *            I                                L            2                                              (        1        )            wherein E is Young's modulus and I is the moment of inertia. For a quadratic cross section, the value of I is proportional to the cube of the thickness, so the danger of mechanical failure increases as a fast function of the reduction in thickness of a protrusion. Confirmation of this fact can be found in that it has been known in the flexographic industry that small dots on flexographic printing plates tend to break off or wear easily, resulting in discontinuities in tone gradation near the highlights.
Gravure rolls are manufactured by an expensive and time consuming etching process or by means of a diamond stylus which embosses a gravure roll.
European patent application with publication number EP 1 428 666 by Verhoest et al teaches making a flexographic printing plate using an inkjet apparatus. The plate is formed by applying subsequently on a substrate at least two image-wise layers of polymerisable ink by an inkjet printer. Between the application of the first and second layers, the first layer is immobilized by initiating a polymerization of the ink using a UV source.
European patent application with publication number EP 1 437 882 by Delabastita et al teaches an image processing method for creating a three dimensional print master. According to the invention a binary digital image represents the printing surface of a flexographic printing plate. A topographic operator, such as a circular symmetric smoothing filter, is applied on this binary halftone image resulting in a contone image of which the densities represent the heights of a relief print master. The contone image is then conceptually sliced to obtain intermediate binary layers which, when printed on top of each other, form a three-dimensional print master. The effect of the smoothing filter is that around each pixel in an upper intermediate layer a circle of identical pixels is replicated in a lower intermediate layer. As a result, every lower intermediate layer always entirely supports any upper intermediate layer.
One problem with the latter technique is that it requires many computations. It is therefore desirable to come up with a method to calculate the intermediate layers in a way that requires fewer calculations.